Matched Asymptotic Expansions and Singular Perturbations
Author | : |
Publisher | : Elsevier |
Total Pages | : 153 |
Release | : 2011-08-26 |
Genre | : Mathematics |
ISBN | : 0080871178 |
Matched Asymptotic Expansions and Singular Perturbations
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Author | : |
Publisher | : Elsevier |
Total Pages | : 153 |
Release | : 2011-08-26 |
Genre | : Mathematics |
ISBN | : 0080871178 |
Matched Asymptotic Expansions and Singular Perturbations
Author | : Robert E. Jr. O'Malley |
Publisher | : Elsevier |
Total Pages | : 215 |
Release | : 2012-12-02 |
Genre | : Mathematics |
ISBN | : 0323162274 |
Introduction to Singular Perturbations provides an overview of the fundamental techniques for obtaining asymptomatic solutions to boundary value problems. This text explores singular perturbation techniques, which are among the basic tools of several applied scientists. This book is organized into eight chapters, wherein Chapter 1 discusses the method of matched asymptomatic expansions, which has been frequently applied to several physical problems involving singular perturbations. Chapter 2 considers the nonlinear initial value problem to illustrate the regular perturbation method, and Chapter 3 explains how to construct asymptotic solutions for general linear equations. Chapter 4 discusses scalar equations and nonlinear system, whereas Chapters 5 and 6 explain the contrasts for initial value problems where the outer expansion cannot be determined without obtaining the initial values of the boundary layer correction. Chapters 7 and 8 deal with boundary value problem that arises in the study of adiabatic tubular chemical flow reactors with axial diffusion. This monograph is a valuable resource for applied mathematicians, engineers, researchers, students, and readers whose interests span a variety of fields.
Author | : Lindsay A. Skinner |
Publisher | : Springer Science & Business Media |
Total Pages | : 95 |
Release | : 2011-05-11 |
Genre | : Mathematics |
ISBN | : 1441999582 |
This book is a rigorous presentation of the method of matched asymptotic expansions, the primary tool for attacking singular perturbation problems. A knowledge of conventional asymptotic analysis is assumed. The first chapter introduces the theory and is followed by four chapters of applications to ordinary differential equation problems of increasing complexity. Exercises are included as well as several Maple programs for computing the terms of the various asymptotic expansions that arise in solving the problems.
Author | : A. M. Ilʹin A. M. Il'in |
Publisher | : American Mathematical Soc. |
Total Pages | : 754 |
Release | : 1992 |
Genre | : Asymptotic expansions |
ISBN | : 9780821897348 |
Author | : E. J. Hinch |
Publisher | : Cambridge University Press |
Total Pages | : 178 |
Release | : 1991-10-25 |
Genre | : Mathematics |
ISBN | : 9780521378970 |
A textbook presenting the theory and underlying techniques of perturbation methods in a manner suitable for senior undergraduates from a broad range of disciplines.
Author | : Mark H. Holmes |
Publisher | : Springer Science & Business Media |
Total Pages | : 344 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1461253470 |
This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.
Author | : Milton Van Dyke |
Publisher | : Parabolic Press, Incorporated |
Total Pages | : 296 |
Release | : 1975 |
Genre | : Science |
ISBN | : |
Author | : P.A. Lagerstrom |
Publisher | : Springer Science & Business Media |
Total Pages | : 263 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475719906 |
Content and Aims of this Book Earlier drafts of the manuscript of this book (James A. Boa was then coau thor) contained discussions of many methods and examples of singular perturba tion problems. The ambitious plans of covering a large number of topics were later abandoned in favor of the present goal: a thorough discussion of selected ideas and techniques used in the method of matched asymptotic expansions. Thus many problems and methods are not covered here: the method of av eraging and the related method of multiple scales are mentioned mainly to give reasons why they are not discussed further. Examples which required too sophis ticated and involved calculations, or advanced knowledge of a special field, are not treated; for instance, to the author's regret some very interesting applications to fluid mechanics had to be omitted for this reason. Artificial mathematical examples introduced to show some exotic or unexpected behavior are omitted, except when they are analytically simple and are needed to illustrate mathematical phenomena important for realistic problems. Problems of numerical analysis are not discussed.
Author | : Carl M. Bender |
Publisher | : Springer Science & Business Media |
Total Pages | : 605 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475730691 |
A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
Author | : W. Eckhaus |
Publisher | : Elsevier |
Total Pages | : 301 |
Release | : 2011-08-30 |
Genre | : Mathematics |
ISBN | : 0080875300 |
Asymptotic Analysis of Singular Perturbations